Lenticular lens, light-diffusing sheet, and projection screen

ABSTRACT

A lenticular lens  23  comprises multiple convex unit lenses  23   b , two sides of each unit lens  23   b  being curved surfaces gradually spreading outwardly from the upside (plane of emergence) to the base (plane of incidence) of the unit lens, and these unit lenses  23   b  are disposed on a base film  21  in parallel with each other. The acute angle θ between a tangent to two curves corresponding to the two sides of the unit lens  23   b  on its section vertical to the longer direction and a line parallel to the upside (or the base) of the unit lens  23   b  is in a range represented by the following inequality: 
       139( d/p ) 3 −176( d/p ) 2 +78( d/p )+74.4&gt;θ&gt;346( d/p ) 3 −469( d/p ) 2 +219( d/p )+45.0 
     where d is the length of half of the distance between the two curves, and p is the pitch at which the unit lenses are disposed.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a lenticular lens, to a light-diffusingsheet, and to a projection screen.

2. Background Art

In a rear projection display, an image produced by image light emerging(projected) from a light source set at the rear of the display isdisplayed on a projection screen mounted on the front of the display.

A cross-sectional view of a lenticular lens, a component part of aprojection screen, is shown in FIG. 7 in Patent Document 1. Thelenticular lens has, on one side, multiple unit lenses 11 in the shapeof trapezoidal prisms, and a pair of oblique sides of a trapezoidalcross section of each unit lens 11 are curved.

By making a pair of slanting surfaces (oblique sides on across-sectional view) of each one of the multiple unit lenses 11 on oneside of the lenticular lens curved, it is possible to improve theuniformity of light emerging from the projection screen.

Patent Document Japanese Laid-Open Patent Publication No. 2004-294465

SUMMARY OF THE INVENTION

An object of the present invention is to provide the specific shape of apair of slanting surfaces (curved surfaces) of a unit lens with whichemerging light that is uniform in luminosity and that is bright whenviewed even from an oblique direction (that can be observed withoutdifficulty even from an oblique direction) can be obtained.

Another object of the present invention is to provide a lenticular lens,a light-diffusing sheet, and a projection screen that are useful forobtaining emerging light that is uniform in luminosity and that isbright when viewed even from an oblique direction (that can be observedwithout difficulty even from an oblique direction).

The present invention is a lenticular lens formed on a base film,comprising multiple convex unit lenses disposed on the base film withtheir long sides parallel to each other, the two edges of each unit lenson its section vertical to the longer direction being a pair of curvesspreading outwardly from the upside of the cross section, situated onthe side opposite to the base film, to the base of the cross section,situated on the base film side, the angle θ between a tangent to thecurves of each unit lens and a line parallel to the upside and base ofthe unit lens being acute, the angle θ with any line parallel to theupside and base of the unit lens being in a range represented by thefollowing inequality:

139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0

where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.

The present invention is the lenticular lens in which the acute angle θis in a range represented by the following inequality:

−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546>θ>−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086.

The present invention is the lenticular lens in which a space betweeneach two adjacent unit lenses is filled with a resin having a refractiveindex lower than that of the unit lenses.

The base film is in sheet form, and on this base film are formed themultiple unit lenses. Each unit lens is convex and has a pair of obliquesides (two sides), the upside, and the base. Light (image light) entersthe unit lens from the base and emerges from the upside. The upside(plane of emergence) and base (plane of incidence) of the unit lens arenearly parallel to each other, and the two oblique sides of the unitlens connect the two ends of the upside (plane of emergence) of the unitlens and those of the base (plane of incidence) of the unit lens,respectively. The width of the upside (plane of emergence) of the unitlens is narrower than that of the base (plane of incidence) of the unitlens, and the two oblique sides of the unit lens are in the shape ofcurved surfaces gradually spreading outwardly from the upside to thebase. The horizontal position of the upside (plane of emergence) of theunit lens is nearly the center of the base (plane of incidence) of theunit lens.

The section of the unit lens, vertical to the longer direction, isnearly trapezoidal. Since the unit lens gradually spreads outwardly fromits upside (plane of emergence) to its base (plane of incidence), theoblique sides of the trapezoidal section, vertical to the longerdirection, of the unit lens (corresponding to the two oblique sides ofthe unit lens) are a pair of nearly symmetrical curves spreadingoutwardly. In an embodiment, a groove between each two adjacent unitlenses is filled with a resin having a refractive index lower than thatof the unit lenses.

In this invention, the shape of a pair of oblique sides (curvedsurfaces) of the unit lens is specified by the acute angle θ between atangent to a pair of curves showing the two oblique sides of the unitlens on its section vertical to the longer direction and a line parallelto the upside and base of the unit lens. The two oblique sides (curves)are curved surfaces (curved lines) gradually spreading outwardly, sothat the acute angle with a curve situated near the plane of emergenceof the unit lens (the short side of the trapezoidal cross section) neverexceeds the acute angle with a curve situated near the plane ofincidence of the unit lens (the long side of the trapezoidal crosssection).

The range of the acute angle θ was determined in the light of thefollowing two points.

(1) The acute angle θ must be in such a range that emerging lightproviding only one positive half value angle can be obtained.

The half value angle is an angle (angle of observation) at which therelative brightness is 0.5, when the brightness value at the horizontalangle (angle of observation) at which light with maximum luminosity(brightness) emerges (in general, in the center of a screen (angle ofobservation=0°)) is taken as 1. The angle of observation includespositive angle of observation (right-hand side of a viewer) and negativeangle of observation (left-hand side of a viewer). When emerging lightprovides only one positive half value angle (as well as one negativehalf value angle), no huge variations occur in luminosity.

(2) The half value angle must be equal to or greater than apredetermined angle.

A greater half value angle makes it possible to view a relatively brightimage even when a screen provided with the lenticular lens is observedfrom an oblique direction.

By making the shape of a pair of oblique sides (curved surfaces) of theunit lens so that the angle θ falls in the angle range specified in thepresent invention, there can be obtained emerging light that providesonly one half value angle, and the horizontal uniformity of emerginglight can thus be improved. Further, even when the light is observedfrom a relatively oblique direction, a bright image can be viewed.

The present invention also provides a light-diffusing sheet having thefollowing definition.

The present invention is a light-diffusing sheet comprising a lenselement sheet containing a base film, a prism lens formed on one surfaceof the base film and a lenticular lens formed on the other surface ofthe base film, and a support laminated to the lens element sheet, whereparallel light entering the light-diffusing sheet from the prism lensside emerges from the support side, characterized in that the lenticularlens has multiple convex unit lenses disposed on the base film withtheir long sides parallel to each other, that the two edges of each unitlens on its section vertical to the longer direction are a pair ofcurves spreading outwardly from the upside of the cross section,situated on the side opposite to the base film, to the base of the crosssection, situated on the base film side, and that a space between eachtwo adjacent unit lenses is filled with a resin having a refractiveindex lower than that of the unit lenses.

The present invention is the light-diffusing sheet in which thelenticular lens has such a structure that light emerging from thesupport provides only one positive half value angle.

The present invention is the light-diffusing sheet in which thelenticular lens has such a structure that light emerging from thesupport provides a positive half value angle of 35° or more.

The present invention is the light-diffusing sheet in which thelenticular lens provides only one positive half value angle, and thepositive half value angle is 35° or more.

The present invention is the light-diffusing sheet in which thelenticular lens makes light emerge from the support so that the emerginglight has such a luminosity distribution that the luminosity decreasesalmost monotonically as the angle of observation increases.

The present invention is the light-diffusing sheet in which the angle θbetween a tangent to the curves of each unit lens and a line parallel tothe upside and base of the unit lens is acute, and the angle θ with anyline parallel to the upside and base of the unit lens is in a rangerepresented by the following inequality:

139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0

where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.

The present invention is the light-diffusing sheet in which the acuteangle θ is in a range represented by the following inequality:

−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546>θ>−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086.

Between the lens element sheet and the support may be present othermember (e.g., an adhesive resin, etc.).

By designing the lenticular lens (unit lenses) so that the acute angle θfalls in the above-described angle range, there can be obtained emerginglight having such a luminosity distribution (gain curve) that theluminosity decreases almost monotonically as the angle of observationincreases (the absolute value of the angle of observation when adistinction is made between the angle of observation on the left-handside and that on the right-hand side by putting “positive (plus)” and“negative (minus)” to the angles of observation, respectively) (emerginglight that gradually gets darker as the angle of observation graduallyincreases).

The present invention is a projection screen comprising a Fresnel lensand a lenticular lens, the lenticular lens being formed on a base filmand comprising multiple convex unit lenses disposed on the base filmwith their long sides parallel to each other, the two edges of each unitlens on its section vertical to the longer direction being a pair ofcurves spreading outwardly from the upside of the cross section,situated on the side opposite to the base film, to the base of the crosssection, situated on the base film side, the angle θ between a tangentto the curves of each unit lens and a line parallel to the upside andbase of the unit lens being acute, the angle θ with any line parallel tothe upside and base of the unit lens being in a range represented by thefollowing inequality:

139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0

where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.

The present invention is a projection screen comprising a Fresnel lensand a light-diffusing sheet, the light-diffusing sheet comprising a lenselement sheet containing a base film, a prism lens formed on one surfaceof the base film and a lenticular lens formed on the other surface ofthe base film, and a support laminated to the lens element sheet, whereparallel light entering the light-diffusing sheet from the prism lensside emerges from the support side, characterized in that the lenticularlens has multiple convex unit lenses disposed on the base film withtheir long sides parallel to each other, that the two edges of each unitlens on its section vertical to the longer direction are a pair ofcurves spreading outwardly from the upside of the cross section,situated on the side opposite to the base film, to the base of the crosssection, situated on the base film side, and that a space between eachtwo adjacent unit lenses is filled with a resin having a refractiveindex lower than that of the unit lenses.

The present invention is the projection screen in which the angle θbetween a tangent to the curves of each unit lens and a line parallel tothe upside and base of the unit lens is acute, and the angle θ with anyline parallel to the upside and base of the unit lens is in a rangerepresented by the following inequality:

139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0

where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatical view showing the internal structure of aprojection display.

FIG. 2 is a perspective view of a light-diffusing sheet.

FIG. 3 is a sectional view taken along line III-III of FIG. 2.

FIG. 4 is a diagram showing the relationship between the horizontalangle (angle of observation) and the luminosity of light emerging from aprojection screen having unit lenses, two sides of each unit lens beingflat or curved slanting surfaces.

FIG. 5 is a view showing the relationship between the x and ycoordinates and the curves on a cross section of unit lenses.

FIG. 6 is a view showing on the x and y coordinates the cross-sectionalshapes of unit lenses expressed by five functional equations.

FIG. 7 is a diagram showing the relationship between the horizontalangle (angle of observation) and the luminosity of light emerging from aprojection screen comprising a lenticular lens composed of unit lenses,each unit lens being in the shape expressed by one of five functionalequations.

FIG. 8 is a diagram showing the relationship between the value obtainedby dividing, by the pitch p, the length d of half of the distancebetween the two curves of a unit lens in the shape expressed by one offive functional equations and the taper angle θ.

FIG. 9 is a graph showing the upper and lower limits of the taper angleθ specifying the shape of the two sides of slanting surfaces of a unitlens so that emerging light has such a luminosity distribution that theluminosity decreases almost monotonically as the angle of observationincreases.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a view diagrammatically showing the internal structure of arear projection display 1.

The rear projection display 1 is that image light emerging (projected)from a projector (light source) 2 is projected on a projection screen 10mounted on the front of the projection display 1 to display, on thesurface of the projection screen 10, an image (still or moving image)produced by the image light. The projection screen 10 is composed of alight-diffusing sheet 20 and a Fresnel lens 30 placed over it. The imagelight projected from the projector 2 is reflected from a mirror 3 placedinside the projection display 1 and emerges from the projection display1 to the outside via the Fresnel lens 30 and the light-diffusing sheet20 (an image is displayed on the light-diffusing sheet 20). The surfaceof the projection screen 10 (as well as the surface of the Fresnel lens30 and that of the light-diffusing sheet 20) on which image lightprojected from the projector 2 is incident is hereinafter referred to asa “plane of incidence”. The surface of the projection screen 10 (as wellas the surface of the Fresnel lens 30 and that of the light-diffusingsheet 20) from which the image light that has entered the plane ofincidence emerges is hereinafter referred to as a “plane of emergence”.

The projection screen 10 is set on the frame 1 a of the projectiondisplay 1, and, as mentioned above, constitutes a screen of theprojection display 1. The projection screen 10 comes under the categoryof transmission screens because image light that has entered theprojection screen 10 from its plane of incidence emerges from its planeof emergence.

FIG. 2 is a perspective view of the light-diffusing sheet 20constituting the projection screen 10, and FIG. 3 shows a sectional viewtaken along line III-III of FIG. 2, together with the projector 2 (lightsource). In FIG. 2, the light-diffusing sheet 20 is depicted with itshorizontal length (breadth) and vertical length (height) shortened, forconvenience' sake.

The light-diffusing sheet 20 comprises a base film 21, a prism lens 22formed on the plane of incidence of the base film 21, and a lenticularlens 23 formed on the plane of emergence of the base film 21. A support25 useful in fixing the light-diffusing sheet 20 (projection screen 10)to the projection display 1 is provided on the plane of emergence of thelenticular lens 23 with an UV adhesive resin 24 between them.

The image light emerging from the projector 2 is reflected from themirror 3 and enters the Fresnel lens 30 (see FIG. 1). The Fresnel lens30 controls the direction of the image light incident on it so that thelight travels in the direction of the normal to the plane of incidence(plane of emergence) of the projection screen 10 (light travelling inthe direction of the normal to the plane of incidence (plane ofemergence) of the projection screen 10 is usually referred to asparallel light). The parallel image light enters the prism lens 22 inthe light-diffusing sheet 20.

Multiple projecting (trigonal prismatic) unit lenses 22 a whose longerdirection corresponds to the vertical direction of the projection screen10 are disposed side by side on the plane-of-incidence side of the prismlens 22. The prism lens 22 horizontally splits the parallel lightemerging from the Fresnel lens 30 (the representation of splitting ofthe light by the prism lens 22 is omitted from FIG. 3).

The image light that has emerged from the prism lens 22 passes throughthe base film 21 and enters the lenticular lens 23.

The lenticular lens 23 is useful for diffusing the incident image lightmainly in the transverse direction of the projection screen 10 (towardsboth the left- and right-hand sides of a viewer looking at the plane ofemergence of the projection screen 10). On the plane-of-emergence-sideof the lenticular lens 23, there are V-shaped grooves 23 whose longerdirection corresponds to the vertical direction of the projection screen10 (the direction of the height of the projection screen 10, or thevertical direction for a viewer looking at the plane of emergence).Microscopically, the bottom of the V-shaped groove 23 a is flat and ispositioned slightly above the base of the lenticular lens 23 (the depthof the V-shaped groove 23 a is less than the height of the lenticularlens 23). The lenticular lens 23 has, on the plane of emergence of thebase sheet 21, multiple convex unit lenses 23 b whose longer directioncorresponds to the vertical direction of the projection screen 10, andthe unit lenses 23 b are disposed in parallel with each other on thebase sheet 21 with a substrate (covering, joining part) 23 c between theunit lenses 23 b and the base sheet 21. The section of the unit lens 23b (see FIG. 3), vertical to the longer direction, is nearly trapezoidal.Image light enters the base (long side) 23 e, situated on the side ofthe base film 21, of the trapezoidal cross section of the unit lens 23b, and emerges from the upside (short side) 23 f, situated on the sideopposite to the base film 21, of the trapezoidal cross section.

The V-shaped grooves 23 a are filled with a low-refractive-index memberto which light-absorbing particles (indicated by black dots in FIG. 3)are added. The low-refractive-index member has a refractive index lowerthan that of the lenticular lens 23. The low-refractive-index member towhich light-absorbing particles are added is usually black in color, andwhen the lenticular lens 23 in which the V-shaped grooves 23 a arefilled with the low-refractive-index member is viewed from the front, itlooks as if it had a large number of black lines on its surface. TheV-shaped grooves 23 a filled with the low-refractive-index member aretherefore called black stripes (BS's). The V-shaped grooves 23 a filledwith the low-refractive-index member are hereinafter referred to as BS's23 a.

Almost all image light incident on the boundaries between the unitlenses 23 b and the BS's 23 a is reflected (total reflection). The imagelight entering the BS's 23 a without being reflected is absorbed by thelight-absorbing particles added to the low-refractive-index member.

The two oblique sides of the unit lens 23 b consist of a pair of curvedsurfaces (on the cross section of the unit lens 23, a pair of curvedlines) spreading outwardly (in FIGS. 2 and 3, as well as in FIG. 5 thatwill be described later, the curved surfaces (curved lines) areexaggerated for easy understanding). The curved surfaces (curved lines)are in the shape that fulfills predetermined requirements (which will beclarified in the descriptions below).

The image light horizontally diffused by the lenticular lens 23 passesthrough the UV adhesive resin 24 and the support 25, and emerges fromthe light-diffusing sheet 20 to the outside.

The shape of the two sides (two slanting surfaces) of the unit lens 23 bwill now be described.

By making the two sides (two slanting surfaces) of the unit lens 23 bcurved, the uniformity of the horizontal luminosity (brightness) oflight emerging from the plane of emergence of the projection screen 10can be made higher, as compared with the case where the two surfaces ofthe unit lens 23 b are made flat. FIG. 4 shows the relationship (gaincurve) between the horizontal angle (angle of observation) and theluminosity of light emerging from the projection screen 10. In FIG. 4,the dotted line shows the case where the two sides of slanting surfacesof the unit lens 23 b are flat, while the thick, solid line shows thecase where the two sides of slanting surfaces of the unit lens 23 b arecurved.

As shown in FIG. 4, when the slanting surfaces of the unit lens 23 b aremade curved, the horizontal luminosity of light emerging from theprojection screen 10 becomes more uniform (luminosity distributionbecomes smooth) as compared with the case where the slanting surfaces ofthe unit lens 23 b are made flat. Variations of luminosity with theposition of observation are reduced, so that the projection screen 10can display a clear image.

In the technical field of projection screens, the half value angle isused as a measure of variations of luminosity with the position ofobservation. The half value angle is an angle (angle of observation) atwhich the relative brightness is 0.5, when the brightness at thehorizontal angle (angle of observation) at which light with maximumluminosity (brightness) emerges (in general, in the center of a screen(angle of observation=0°)) is taken as 1.

If only positive angles (angles of observation of 0° or more in FIG. 4)are considered, it can be said that variations of luminosity with theposition of observation are great when two or more positive half valueangles exist. It is therefore preferred that only one positive halfvalue angle be present at positive angles.

Further, when the half value angle is greater, a relatively bright imagecan be viewed even when the projection screen is observed from anoblique direction. The greater the positive half value angle, the moreadvantageous.

The applicant tried to determine, by carrying out simulations, the shapeof the two sides of slanting surfaces of the unit lens 23 b with whichemerging light fulfilling the requirements that emerging light providesonly one positive half value angle (not two or more) and that thepositive half value angle is 35° or more (these two requirements beingcollectively referred to as the “requirement for optimization”) can beobtained.

The shape of a pair of curves 23 i showing the two oblique sides of theunit lens 23 b on its section vertical to the longer direction of theunit lens 23 b can be specified by a functional equation on twodimensional (x-y) coordinates. In simulation for determining the shapeof the curves, the shape of the curves is specified by a functionalequation; the brightness of light emerging from a lenticular lens 23composed of unit lenses 23 b, designed so that each unit lens 23 b has,on its cross section, curves fulfilling the functional equation, isdetermined by changing the angle of observation; and the shape of thecurves (functional equation) is corrected so that it meets theabove-described requirement for optimization.

In the correction of the shape of the curves, the angle (hereinafterreferred to as the taper angle θ) of a pair of curves 23 i (hereinafterreferred to simply as curves of the unit lens 23) (the acute anglebetween a tangent to the curves of the unit lens 23 b and a lineparallel to the plane of incidence (the base) (or the plane of emergence(the upside)) of the unit lens 23 b) showing the two oblique sides ofthe unit lens 23 b on its section vertical to the longer direction isused as a variable. This is because it is possible to control theluminosity (brightness) at the desired angle of observation by adjustingthe taper angle θ. In the simulation, the shape of the curves(functional equation) initially set is subjected to recalculation sothat the unit lens 23 b has the taper angle θ adjusted. It is needlessto say that the taper angle θ varies depending upon the point on thecurves of the unit lens 23 b, at which the taper angle θ is determined.Further, as will be described later, the taper angle θ is specified bythe width of the plane of incidence of the unit lens 23 b (the length ofthe base (long side) of the trapezoidal cross section) (hereinafterreferred to as a pitch p at which the unit lenses are disposed) and thelength d of half of the distance between the above-described pair ofcurves 23 i (hereinafter also referred to as a “distance”).

Linear functions are excluded from functional equations to be initiallyset to express the curves 23 i of the unit lens 23 b. This is becausethe shape of a curve cannot be specified by a linear function. Further,a functional equation containing a term with an odd exponent (x, x³, x⁵,etc.) cannot express a curve that shows the opposing oblique sides ofthe unit lens 23 b. For this reason, a quadratic or higher function(polynomial function) containing terms with even exponents only is usedas a functional equation for specifying the initial shape (beforecorrection) of the curves of the unit lens 23 b. Drawn by such afunctional equation initially set is a parabola (a curve graduallyspreading outwardly) with its apex on the y-axis.

Explanation of the simulation results will be given below. In thisexample, the following five functional equations (equations specifyingthe shape of the curves of the above-described unit lens 23 b) will berepresentatively described.

y=2·10⁻⁸ x ⁶−9·10⁻⁵ x ⁴+0.4172x ²−37.709  Functional equation (1)

y=−5·10⁻⁵ x ⁴+0.2860x ²−23.745  Functional equation (2)

y=6·10⁻⁵ x ⁴+0.1583x ²−14.325  Functional equation (3)

y=−2·10⁻⁵ x ⁴+0.1619x ²−13.993  Functional equation (4)

y=−2·10⁻⁵ x ⁴+0.1286x ²−10.828  Functional equation (5)

FIG. 6 shows the functional equations (1) to (5) on the x and ycoordinates. In FIG. 6, the trapezoidal sections of unit lenses 23 b areshown with the bases (long sides) of the trapezoids trued up. Therefore,the position of the x-axis (the position of the upside (short side) ofthe trapezoidal cross section of the unit lens 23 b) varies dependingupon the functional equation. Further, in the simulation, the width ofthe plane of incidence of the unit lens 23 b (the length of the base(long side) of the trapezoidal section) (pitch p) is set to 1 mm, andthe width of the plane of emergence of the unit lens 23 b (the length ofthe upside (short side) of the trapezoidal section) is set to 0.3 mm.With the above-described flat bottom of the V-shaped groove taken intoconsideration, the sum total of the width of the plane of incidence ofthe unit lens 23 b and the width of the flat bottom of the V-shapedgroove may also be taken as the pitch p. The width of the plane ofincidence of the unit lens 23 b (pitch p) and the width of the plane ofemergence of the unit lens 23 b may, of course, be freely adjusted(according to the results of measurement, etc.).

FIG. 7 shows the results of the simulation, that is, the relationshipbetween the horizontal angle of observation (positive angles only) andthe luminosity of light emerging from a projection screen 10 containinga lenticular lens 23 with unit lenses 23 b, the curves of each unit lens23 b being in the shape specified by one of the above-described fivefunctional equations. Shown in FIG. 7 are graphs of luminosity plottedagainst positive angles of observation. Graphs of luminosity plottedagainst negative angles of observation are symmetrical to the graphsshown in FIG. 7.

When a lenticular lens 23 composed of unit lenses 23 b specified by theabove-described functional equation (1) was used, the half value anglewas less than 35°, and the aforementioned requirement for optimizationwas not fulfilled. When a lenticular lens 23 composed of unit lenses 23b specified by the functional equation (5) was used, more than two halfvalue angles were present, so that the requirement for optimization wasnot fulfilled.

On the other hand, when a lenticular lens 23 composed of unit lenses 23b specified by the functional equation (2), (3), or (4) was used, therequirement for optimization was fulfilled.

FIG. 8 shows graphs (thick lines) showing the relationship between thevalue (abscissa axis) obtained by dividing, by the pitch p, the length dof half of the distance between a pair of curves 23 i, i.e., between thetwo intersections of curves 23 i and a line 23 g parallel to the upside23 f and base 23 e of the unit lens 23 b (in FIGS. 5 and 6, the distancefrom the y-axis) and the above-described taper angle θ (ordinate axis)(unit: Deg.). As mentioned above, in this simulation, the pitch p is setto 1 mm, and the width of the plane of emergence of the unit lens 23 b(the length of the upside (short side) of the trapezoidal cross section)is set to 0.3 mm, so that the taper angle θ is plotted against d/p ratioranging from 0.15 to 0.5.

A lenticular lens 23 composed of unit lenses 23 b specified by thefunctional equation (1) or (5) does not fulfill the requirement foroptimization, as described above. However, in the graph showing therelationship between the “distance d/pitch p” ratio and the taper angleθ (FIG. 8), the curves below the curve of the functional equation (1)practically fulfills the above-described requirement for optimization,and the curves above the curve of the functional equation (5)practically fulfills the requirement for optimization.

In the graph showing the relationship between the “distance d/pitch p”ratio and the taper angle θ (FIG. 8), the curve (approximate curve)drawn when the unit lens 23 b is in the shape specified by thefunctional equation (1) is expressed by the following equation.

Taper angle θ=139(d/p)³−176(d/p)²+78(d/p)+74.4

In the graph showing the relationship between the “distance d/pitch p”ratio and the taper angle θ (FIG. 8), the curve (approximate curve)drawn when the unit lens 23 b is in the shape specified by thefunctional equation (5) is expressed by the following equation.

Taper angle θ=346(d/p)³−469(d/p)²+219(d/p)+45.0

Namely, as long as the curves of the unit lens 23 b have, with any line23 g parallel to the upside 23 f and base 23 e of the unit lens 23 b, ataper angle θ that fulfills the following inequality, it can be saidthat the curves practically meet the above-described requirement foroptimization.

139(d/p)³−176(d/p)²+78(d/p)+74.4>taper angleθ>346(d/p)³−469(d/p)²+219(d/p)+45.0

Thus, the shape of a pair of curves 23 i of the unit lens 23 b (theshape of two oblique sides of the unit lens 23 b) that fulfills therequirement for optimization can be specified in terms of taper angle θ.Since the two slanting surfaces of the unit lens 23 b are curvedsurfaces gradually spreading outwardly, the acute taper angle with acurve situated near the plane of emergence of the unit lens 23 b neverexceeds the angle with a curve situated near the plane of incidence.

In the above-described example, the shape of the two sides of slantingsurfaces of the unit lens 23 b, with which emerging light fulfilling therequirement for optimization that emerging light provides only onepositive half value angle (not two or more half value angles) and thatthe positive half value angle is 35° or more can be obtained, isspecified by the taper angle θ range. The taper angle θ range mayfurther be defined so that emerging light has such a luminositydistribution that the luminosity decreases almost monotonically as theangle of observation (the absolute value of the angle of observation)increases (see the graph (thick line) showing the case where the“slanting surfaces are curved surfaces” in FIG. 4). As a result of thesimulation, it was found that the slanting surfaces (curved surfaces) ofthe unit lens 23 b, with which there can be obtained imaging lighthaving such a luminosity distribution that the luminosity decreasesalmost monotonically as the angle of observation increases, were in sucha shape that the taper angle θ is in a range represented by thefollowing inequality.

−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546>taper angleθ>−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086.

FIG. 9 is a graph showing the relationship between the “distance d/pitchp” ratio and the taper angle θ. In this figure, the curves of thefunctional equations (1) to (5) are shown together with the curvesindicating the upper and lower limits of the taper angle θ specifyingthe shape of the slanting surfaces (curved surfaces) of the unit lens 23b with which there can be obtained emerging light having such aluminosity distribution that the luminosity decreases nearlymonotonically as the angle of observation increases. In FIG. 9, thegraph denoted by symbol A (taper angleθ=−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546) shows theupper limit of the taper angle θ, and the graph denoted by symbol C(taper angleθ=−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086), the lowerlimit of the taper angle θ. The graph denoted by symbol B (taper angleθ=−2252.5(d/p)⁴+3310.7(d/p)³−1850.9(d/p)²+492.64(d/p)+29.001) liesbetween the graph denoted by symbol A and that denoted by symbol C. Inorder to obtain emerging light having such a luminosity distributionthat the luminosity decreases almost monotonically as the angle ofobservation increases, it is preferable to from the unit lenses 23 b sothat they have the taper angle θ denoted by symbol B.

1. A lenticular lens formed on a base film, comprising: multiple convexunit lenses disposed on the base film with their long sides parallel toeach other, the two edges of each unit lens on its section vertical tothe longer direction being a pair of curves spreading outwardly from theupside of the cross section, situated on the side opposite to the basefilm, to the base of the cross section, situated on the base film side,the angle θ between a tangent to the curves of each unit lens and a lineparallel to the upside and base of the unit lens being acute, the angleθ with any line parallel to the upside and base of the unit lens beingin a range represented by the following inequality:139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.
 2. Thelenticular lens according to claim 1, wherein the acute angle θ is in arange represented by the following inequality:−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546>θ>−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086.3. The lenticular lens according to claim 1, wherein a space betweeneach two adjacent unit lenses is filled with a resin having a refractiveindex lower than that of the unit lenses.
 4. A light-diffusing sheetcomprising: a lens element sheet containing a base film, a prism lensformed on one surface of the base film, and a lenticular lens formed onthe other surface of the base film, and a support laminated to the lenselement sheet, where parallel light entering the light-diffusing sheetfrom the prism lens side emerges from the support side, characterized inthat the lenticular lens has multiple convex unit lenses disposed on thebase film with their long sides parallel to each other, that the twoedges of each unit lens on its section vertical to the longer directionare a pair of curves spreading outwardly from the upside of the crosssection, situated on the side opposite to the base film, to the base ofthe cross section, situated on the base film side, and that a spacebetween each two adjacent unit lenses is filled with a resin having arefractive index lower than that of the unit lenses.
 5. Thelight-diffusing sheet according to claim 4, wherein the lenticular lenshas such a structure that light emerging from the support provides onlyone positive half value angle.
 6. The light-diffusing sheet according toclaim 4, wherein the lenticular lens has such a structure that lightemerging from the support provides a positive half value angle of 35° ormore.
 7. The light-diffusing sheet according to claim 4, wherein thelenticular lens provides only one positive half value angle, and thepositive half value angle is 35° or more.
 8. The light-diffusing sheetaccording to claim 4, wherein the lenticular lens makes light emergefrom the support so that the emerging light has such a luminositydistribution that the luminosity decreases almost monotonically as theangle of observation increases.
 9. The light-diffusing sheet accordingto claim 4, wherein the angle θ between a tangent to the curves of eachunit lens and a line parallel to the upside and base of the unit lens isacute, and the angle θ with any line parallel to the upside and base ofthe unit lens is in a range represented by the following inequality:139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.
 10. Thelight-diffusing sheet according to claim 9, wherein the acute angle θ isin a range represented by the following inequality:−2252.5(d/p)⁴+3220.6(d/p)³−1752.9(d/p)²+456.61(d/p)+34.546>θ>−2252.5(d/p)⁴+3400.8(d/p)³−1951.6(d/p)²+530.66(d/p)+23.086.11. A projection screen comprising: a Fresnel lens, and a lenticularlens, the lenticular lens being formed on a base film and comprisingmultiple convex unit lenses disposed on the base film with their longsides parallel to each other, the two edges of each unit lens on itssection vertical to the longer direction being a pair of curvesspreading outwardly from the upside of the cross section, situated onthe side opposite to the base film, to the base of the cross section,situated on the base film side, the angle θ between a tangent to thecurves of each unit lens and a line parallel to the upside and base ofthe unit lens being acute, the angle θ with any line parallel to theupside and base of the unit lens being in a range represented by thefollowing inequality:139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.
 12. Aprojection screen comprising: a Fresnel lens, and a light-diffusingsheet, the light-diffusing sheet comprising: a lens element sheetcontaining a base film, a prism lens formed on one surface of the basefilm, and a lenticular lens formed on the other surface of the basefilm, and a support laminated to the lens element sheet, where parallellight entering the light-diffusing sheet from the prism lens sideemerges from the support side, characterized in that the lenticular lenshas multiple convex unit lenses disposed on the base film with theirlong sides parallel to each other, that the two edges of each unit lenson its section vertical to the longer direction are a pair of curvesspreading outwardly from the upside of the cross section, situated onthe side opposite to the base film, to the base of the cross section,situated on the base film side, and that a space between each twoadjacent unit lenses is filled with a resin having a refractive indexlower than that of the unit lenses.
 13. The projection screen accordingto claim 12, wherein the angle θ between a tangent to the curves of eachunit lens and a line parallel to the upside and base of the unit lens isacute, and the angle θ with any line parallel to the upside and base ofthe unit lens is in a range represented by the following inequality:139(d/p)³−176(d/p)²+78(d/p)+74.4>θ>346(d/p)³−469(d/p)²+219(d/p)+45.0where d is the length of half of the distance between the two curves,and p is the pitch at which the unit lenses are disposed.